It happens on videos on many sites like YouTube. (I joined the html5 beta at YouTube to sort that out, but that doesn't fix other sites.) The crash seems to occur on any site using Adobe Flash, and is becoming very annoying.

I'm using 12.04 with Firefox and used the flash-helper plug-in as well but the same result.

I would mention that I am using Ubuntu 12.04 LTS with various Firefox installs and they are not Crashing, so there is a good possibility that your problem is more specific to your own setup,rather than being a generalized problem.

Is it a crash ?

Note that if it is a crash, (then unless you are on Aurora/Nightly) Firefox will offer to send crash reports, and allow you to obtain Crash IDs. Those are useful for tracking specific reasons for Crashes.

This part of the answer is even more general, but may still help.

It has already been mentioned by "Daniel" that Adobe is not supporting Flash properly on Ubuntu. One effect of this is that Ubuntu users do not have the Latest FlashPlayer release as is used by and causing problems on Firefox Windows systems

So one thing you need NOT worry about are the Firefox issues with Flash 11.3
There will be; what is to Ubuntu users; a lot of noise on the internet relating to these issues and I am aware developers from Flash, Firefox & RealPlayer are involved. (RealPlayer have made a new release which Firefox promptly blocklisted again - soft black I presume - confirmation will be here )

Sorry for posting links but your question is at present rather general, so a general troubleshooting link seems best (There should be no link rot problem, mozilla normally archives rather than deletes Firefox KB articles, or if they are renamed or puts in suitable redirects).

Post back when you have more details and have tried read the linked articles and maybe someone will be able to offer a more specific answer.